The application of linear programming to a coal-mining problem: A case study - W. G. Klerck; G. M.S. Turner (South African Journal of Business Management, 1985)
This article describes the application of linear programming to a problem faced by a small coal-mining company. The company owns two operating collieries, one supplies the general inland trade market while the other supplies a power station under a 30-year-tied contract. The company was awarded an export allocation for a 30-year period and as a result was trying to establish how to supply the coal for the various markets. Only the colliery that supplied the power station had sufficient reserves to base an export contract on. It was underlain by two economically recoverable seams of coal. The quality of the coal reserves is, however, low compared to international standards and is therefore unacceptable in its raw state. It is, however, possible to upgrade the coal by washing it. The grade of the final product (float) can be adjusted by altering the density of washing. However the yield, as a percentage of the raw coal feed, falls off rapidly as the grade is increased. Furthermore the sinks can likewise be upgraded by washing. The company wondered how they should optimize the flowsheet. How much coal should they mine from each of the two seams, how much from each source should go to the power station, how much should they produce for export, how should the upgrading be done, and to what extent. A linear programming model was formulated to solve the problem facing the company.
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